K. F. Tee Department of Aerospace Engineering, University of Bristol, Bristol BS8 1TR, UK A. Spadoni Aerospace, California Institute of Technology, MC 105–50, Pasadena, CA 91125 F. Scarpa 1 Department of Aerospace Engineering, University of Bristol, Bristol BS8 1TR, UK e-mail: f.scarpa@bristol.ac.uk M. Ruzzene School of Aerospace Engineering, Georgia Institute of Technology, Ferst Drive, Atlanta, GA Wave Propagation in Auxetic Tetrachiral Honeycombs This paper describes a numerical and experimental investigation on the flexural wave propagation properties of a novel class of negative Poisson’s ratio honeycombs with tetrachiral topology. Tetrachiral honeycombs are structures defined by cylinders con- nected by four tangent ligaments, leading to a negative Poisson’s ratio (auxetic) behavior in the plane due to combined cylinder rotation and bending of the ribs. A Bloch wave approach is applied to the representative unit cell of the honeycomb to calculate the dispersion characteristics and phase constant surfaces varying the geometric parameters of the unit cell. The modal density of the tetrachiral lattice and of a sandwich panel having the tetrachiral as core is extracted from the integration of the phase constant surfaces, and compared with the experimental ones obtained from measurements using scanning laser vibrometers. DOI: 10.1115/1.4000785 1 Introduction Since the end of the 1940s, honeycomb and sandwich structures have seen a widespread use in aerospace and maritime construc- tions, due to their high stiffness to weight ratio and energy absorp- tion characteristics under static and dynamic impact loading 1. Cellular lattices are also extensively used in space and satellite antennas, and a consistent amount of research has been devolved to the investigation of modal density behavior of sandwich panels linked to its wave propagation properties in aerospace launchers and components, to enhance the vibroacoustic signature and struc- tural integrity of the structures under significant dynamic loading 2. Incidentally, the phononics community has also started to evaluate grid-like artificial periodic arrangements of inclusions and cellular structures 3–6 to develop novel sound management materials, where pass-stop bands characteristics of elastic waves can be used to selective noise filtering capabilities 4. The work on cellular topologies for 2D in-plane and flexural wave propaga- tion has been undertaken as a specific subset of the general wave propagation investigation on periodic structures, where regular tessellation of beams, trusses, and plates were analyzed for civil constructions and aerospace applications 6,7. The concept of a chiral topology was first proposed at molecu- lar level by Wojciechowski 8, and then as structural lattice com- ponent with a Poisson’s ratio -1 by Prall and Lakes 9. Chiral honeycombs are a subset of cellular solids featuring in-plane negative Poisson’s ratio or auxetic behavior. The auxetic behav- ior is used to describe a material that expands laterally when stretched, or conversely contracts laterally when compressed. The unusual negative Poisson’s ratio in cellular materials, in the form of honeycombs, foams, and microporous polymers 10, can be attributed to three aspects: the presence of rotational degrees of freedom, nonaffine deformation kinematics, or anisotropy 11.A typical chiral configuration would have unit cells composed by a central cylinder, with tangent ligaments connecting cylinders from neighboring cells. When subjected to in-plane loading, the cylin- ders would rotate, leading to winding/unwinding of the ligaments, and therefore providing the negative Poisson’s ratio effect. Most of the chiral configurations currently considered in open literature are the hexachiral ones—each cylinder being connected by six tangent ligaments 8,9. Hexachiral cellular structures compressed under flatwise loading have demonstrated enhanced buckling strength, also compared with regular hexagonal honeycombs 12,13. Hexachiral lattices have also shown rotational-type direc- tionality of in-plane and flexural waves, to be used for acoustic filtering 14 and boundary layer control of cellular wingbox un- der dynamic loading 15. Wave directionality and band-gap prop- erties in phonic hexagonal chiral lattices have been also investi- gated with the use of the Bloch wave theorem 16. Recently, different chiral tessellations have been proposed, al- most all leading to the in-plane negative Poisson’s ratio 17. The tetrachiral lattice is one of these specific chiral topologies, where the cylinder is connected by four tangent ligaments Fig. 1. The tetrachiral topology can also be tessellated to provide a cen- tersymmetric configuration antitetrachiral—the whole honey- comb would be constructed simply by translation of the unit cell in the various directions, rather than combined rotations and trans- lations along the tangent directions only 17. Similarly, to hexachiral configurations, tetrachiral lattice topologies are auxetic in the plane, with a Poisson’s ratio of -1 given by the bending deformation of the connected ligaments. The current work describes for the first time the flexural wave propagation characteristics of tetrachiral honeycombs from a nu- merical and experimental point of view. The pass-stop band char- acteristics are determined through the calculations of phase con- stant surfaces determined using a Bloch wave approach 18 implemented in a finite element FE framework 19, while modal properties and modal densities of these cellular lattices are also identified experimentally and compared with the numerical simulations. A tetrachiral honeycomb panel, and a sandwich plate made of quasi-isotropic face skins and the tetrachiral lattice as core constitute the test cases. The sandwich lattice structure is simulated and tested to evaluate the possible use of these cellular phononics as cores for sandwich panels to be used in harsh vi- broacoustic environments. From a design point of view, the pass- stop band characteristics of the tetrachiral lattice can easily be tuned, due to the sensitivity of the phase constant surfaces to the 1 Corresponding author. Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 11, 2009; final manuscript received November 10, 2009; published online April 22, 2010. Assoc. Editor: Jean-Claude Golinval. Journal of Vibration and Acoustics JUNE 2010, Vol. 132 / 031007-1 Copyright © 2010 by ASME Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 06/16/2013 Terms of Use: http://asme.org/terms